Impedance and phase difference of RLC circuit – Rankers Physics
Topic: Alternating Current
Subtopic: LR, RC and LCR Circuits

Impedance and phase difference of RLC circuit

For a series RLC circuit \(R = X_L = 2X_C\). The impedance of the circuit and phase difference between \(V\) and \(i\) will be:
\(\frac{\sqrt{5}R}{2}\text{, } \tan^{-1}(2)\)
\(\frac{\sqrt{5}R}{2}\text{, } \tan^{-1}(1/2)\)
\(\sqrt{5}X_C\text{, } \tan^{-1}(2)\)
\(\sqrt{5}R\text{, } \tan^{-1}(1/2)\)

Solution:

Impedance \(Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2 + (R - R/2)^2} = \frac{\sqrt{5}R}{2}\). Phase difference \(\tan\phi = \frac{X_L - X_C}{R} = 1/2 \Rightarrow \phi = \tan^{-1}(1/2)\).

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